C₃²×D₆₅ #11924065

order	1170
isoclinism	isoclinic class of D₆₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×D₆₅
unambiguous semidirect product	C₅⋊(C₃²×D₁₃)

	subgroup	G/H
center, hypercenter	C₃²	D₆₅
commutator, cosocle, hypocenter	C₅×C₁₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃	C₂
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃²

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 585

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24);(4,5,6)(8,11)(9,10)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)

306 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1170, 23);